Adaptive equalizer

ABSTRACT

An adaptive equalizer processes an input signal that includes noise, pre-cursor intersymbol interference, and post-cursor intersymbol interference. The adaptive equalizer includes a feedforward filter which reduces the pre-cursor intersymbol interference and whitens the noise, a feedback filter which detects the post-cursor intersymbol interference in a signal that corresponds to the input signal, and circuitry which removes the detected post-cursor intersymbol interference from the input signal. The feedforward filter includes separate first and second coefficients. The first coefficients reduce the pre-cursor intersymbol interference and the second coefficients whiten the noise.

TECHNICAL FIELD

[0001] This invention relates to an adaptive equalizer for datacommunications.

BACKGROUND

[0002] Information may be transmitted from a transmitter to a receiverover a communication channel, such as a satellite link, a fiber opticcable, or a copper cable. The information may include, e.g., analogvoice information from a telephone conversation or digital data that istransmitted between two computers. Analog information is oftentransformed into a digital format before it is transmitted over achannel.

[0003] The transmitted information may be encoded into a sequence ofsymbols selected from a set of pre-defined symbols, known as analphabet. Each of the symbols is represented by an electronic pulse,which is transmitted over the communication channel to a remotelocation. The sequence of pulses forms a signal that is received by thereceiver. The receiver retrieves the symbols from the signal and decodesthem to recover the transmitted information.

[0004] Communication channels typically distort the pulses as they aretransmitted through the channels. The channels may add noise to thepulses. Certain types of additive noise, known as white noise, areevenly distributed at all frequencies. Thermal noise from copper wiresis typically a source of white noise. Other types of additive noise,known as colored noise, may be concentrated at certain frequencies.Signals induced on a wire by an adjacent wire, which is known ascrosstalk, are a typical source of colored noise.

[0005] The channel may also distort the amplitude or phase of thetransmitted signals. As a result of this distortion, the pulsesrepresenting the symbols may be corrupted with information from otherpulses in the sequence. The corruption is referred to as inter-symbolinterference (ISI). There are two kinds of ISI. A pulse representing aparticular symbol may be corrupted with information from an earlierpulse in the sequence. This is known as post-cursor ISI. Alternatively,the pulse may be corrupted with information from a future pulse in thesequence. This is known as pre-cursor ISI.

[0006] The receiver typically has a signal detector to detect symbolsreceived from the channel. The detector may, for example, be in the formof a simple threshold detector or a maximum likelihood sequence decoder.The detector is typically optimized to detect symbols that have onlybeen distorted by additive white Gaussian noise (AWGN). Consequently,colored noise and/or inter-symbol interference may cause errors when thesymbols are detected.

DESCRIPTION OF THE DRAWINGS

[0007]FIG. 1 is a block diagram of an adaptive decision feedbackequalizer (DFE).

[0008]FIG. 2 is a block diagram of a feedforward filter in the adaptiveDFE.

[0009]FIG. 3 is a view of a computer system on which coefficients forthe feedforward filter may be determined.

DESCRIPTION

[0010]FIG. 1 shows a block diagram of a channel (h(t)) 10 and anadaptive DFE 12. A signal A_(k), comprised of a sequence of symbols, istransmitted over channel 10 to adaptive DFE 12. The resulting signals(t) contains both pre-cursor and post-cursor ISI. Crosstalk, comprisedof colored noise n(t), is added to s(t) during transmission. Colorednoise (also referred to as “colored Gaussian noise”) is noise thatvaries over a range of frequencies. By contrast, white noise (alsoreferred to as “white Gaussian noise”) is noise that is substantiallythe same over a range of frequencies.

[0011] The combination of s(t) and n(t), namely r(t), is sampled byadaptive DFE 12 at a sampling rate of t₀+kT to produce a discrete timesignal R_(k), where to accounts for the channel delay and sampler phase.R_(k) is applied to feedforward filter (FFF) 14, which produces anoutput signal U_(k). In this embodiment, FFF 14 is finite impulseresponse (FIR) filter that contains a number N_(fff) (N_(fff)≧1) oftaps. Among the N_(fff) taps is a main tap, M (1≦M≦N_(fff)), which isroughly at the center of the taps. FIG. 2 shows a block diagram of FFF14.

[0012] For the purposes of this description, the taps of FFF 14 aredivided into two sets, taps 16 (comprised of the taps from 1 to M) andtaps 18 (comprised of the taps from M+1 to N_(fff)). Taps 16 containcoefficients b_(k) ^(i) (for i=1 to M) that are used by FFF 14 to reducepre-cursor ISI in R_(k). Taps 18 contain different coefficients b_(k)^(i) (for i=M+1 to N_(fff)) that are used by FFF 14 to whiten the noisein R_(k), where the noise is n(t) (sampled, n_(k)) Taps 18 do notnecessarily reduce post-cursor ISI in R_(k). To whiten the noise, thecoefficients on taps 18 reduce the differences in noise n_(k) over therange of frequencies defined by the sampler's Nyquist frequency, kT/2. Adescription of how the coefficients, b_(k) ^(i), are generated isprovided below.

[0013] The output of FFF 14, namely U_(k), contains reduced pre-cursorISI and whitened noise. FBF 20 reduces post-cursor ISI in the output ofadaptive DFE 12. In this embodiment, FBF 20 is an FIR filter thatcontains a number N_(fbf) (N_(fbf)≧1) of taps. The hardware shown in theblock diagram of FIG. 2 may also be used to construct FBF 20. Taps inFBF 20 contain coefficients d_(k) ^(i) (for i=1 to N_(fbf)) that areused by FBF 20 to reduce post-cursor ISI in U_(k). A description of howthe coefficients, d_(k) ^(i), are generated is provided below.

[0014] The feedback loop 22 that includes FBF 20 works as follows. Theoutput of FBF 20, namely Q_(k), is provided to circuit junction 24,which adds Q_(k) to U_(k). The resulting signal Y_(k) containsrelatively little post-cursor ISI (since the post-cursor ISI, Q_(k), isremoved from U_(k)). The signal Y_(k) is applied to slicer 26, whichmakes symbol (e.g., bit) decisions based on the content of Y_(k). Forexample, slicer 26 may determine that a signal having a value that isgreater than “0.0” constitutes a “1” bit and that a signal having avalue that is less than “0.0” constitutes a “0” bit.

[0015] If correct bit decisions are made by slicer 26, the resultingsignal X_(k) will be a replica of A_(k). That is, X_(k) will be the sameas the original data signal A_(k), meaning that X_(k) has no crosstalknoise, pre-cursor ISI, or post-cursor ISI. The difference, or error,between the ideal signal and the received signal is determined by takingthe difference of X_(k) and Y_(k) using circuit junction 28. Asdescribed in more detail below, the error, Ek, is used to adaptivelydetermine the coefficients b_(k) ^(i) for FFF 14 and the coefficientsd_(k) ^(i) for FBF 20.

[0016] The output X_(k) of slicer 26 is also applied to feedback loop30. Feedback loop 30 contains a channel estimator (CE) 32. CE 32 filtersX_(k) to estimate the ISI added by channel 10. In this embodiment, CE 32is an FIR filter with z-domain response, G_(k)(Z). CE 32 performs theappropriate filtering on X_(k), resulting in signal T_(k), whichcorresponds to an estimate of the signal component of R_(k) delayed intime. The amount of the delay is equal to the delay (M+L), where delay Mcorresponds to the delay through FFF 14, circuit junction 24, and slicer26, among other components (not shown), and delay L corresponds to thenumber of precursor samples to be replicated by CE block 32.

[0017] To obtain an estimate, V, of the noise (n_(k)), adaptive DFE 12obtains the difference between T_(k) and a delayed version of R_(k).Delay circuit 34 (Z^((M+L))) delays R_(k) by the delay through adaptiveDFE 12, namely M, and an amount L, which corresponds to the number ofprecursor samples to be replicated by CE 32. T_(k) is the estimate ofthe signal component of R_(k−M−L). Circuit junction 38 subtracts T_(k)from the delayed version of R_(k), namely R_(k−M−L). The resultingsignal, V_(k−M−L), is an estimate of the noise n_(k). V_(k−M−L) isreferred to as an “estimate”, rather than a measurement of the actualnoise, because the value of T_(k) may not exactly match the signalcomponent of R_(k−M−L).

[0018] Described below are examples of ways of generating filter tapcoefficients for FFF 14 and FBF 20. In this regard, prior art processesfor generating pre-cursor and post-cursor tap coefficients for FFF 14generated both types of coefficients in the same manner. Thus, in theprior art, the post-cursor taps of the FFF are designed both to whitennoise and to cancel post-cursor ISI. In a channel that introduces severeISI and colored noise to a signal, such post-cursor taps generallyprevent the FFF from adapting to an optimal weighted matched filter(WMF) solution.

[0019] By contrast, in adaptive DFE 12 described herein, the post-cursortaps of FFF 14 whiten noise, but are not designed to cancel post-cursorISI (although some incidental cancellation of post-cursor ISI mayoccur). Consequently, the pre-cursor and post-cursor taps of FFF 14 areadapted using different least mean square (LMS) processes.

[0020] Referring to FIG. 1, adaptive DFE 12, and the equations thatfollow, are specified for a T-spaced adaptive DFE signal receiverutilizing a real, baseband modulation. To reiterate, in FIG. 1 A_(k):represents transmit data symbols at time index k s (t): representscontinuous time output of the channel h(t) at time t n(t): representsadditive channel noise at time t r(t): represents continuous timereceiver input at time t R_(k): represents sampled receiver input attime index k U_(k): represents the output of FFF 14 B_(k)(z) at timeindex k Q_(k): represents the output of FBF 20 D_(k)(Z) at time index kY_(k): represents the equalized signal at time index k X_(k): representsthe recovered symbol at time index k E_(k): represents the decisionerror (X_(k) − Y_(k)) at time index k h(t): represents thecontinuous-time channel impulse response. The channel is modeled as acontinuous-time impulse response, h(t), with the signal peak at time t₀.B_(k)(z): represents the z-domain response of FFF 14 at time index kD_(k)(z): represents the z-domain response of FFF 14 at time index kV_(k) represents the estimated noise at time index k T_(k) representsthe output of the CE G_(k)(z) at time index k G_(k)(z) represents the CEz-domain response at time index k

[0021] To determine the coefficients, define A_(k) to be a pulseamplitude modulation (PAM) sequence. The received signal r(t) thusconstitutes the superposition of the impulse response of the channelh(t) and each transmitted symbol and the additive noise n(t). The noisemay be either colored or white Gaussian noise. The received signal,r(t), is given as:${r(t)} = {{\sum\limits_{i}{A_{i}{h\left( {t - {iT}} \right)}}} + {{n(t)}.}}$

[0022] The received signal is sampled at instant kT+t₀ to generateR_(k), where t₀ accounts for the channel delay and sampler phase:$R_{k} = {{A_{k}{h\left( t_{0} \right)}} + {\sum\limits_{i \neq k}{A_{i}{h\left( {t_{0} + {kT} - {iT}} \right)}}} + {{n\left( {t_{0} + {kT}} \right)}.}}$

[0023] In this embodiment, FFF 14 is an FIR filter with z-domainresponse${{B_{k}(z)} = {\sum\limits_{i = 1}^{N_{fff}}{b_{k}^{\prime}z^{- i}}}},$

[0024] where N_(fff) is the number of tap coefficients in FFF 14, asdefined above. FBF 20 is an FIR filter with z-domain response${{D_{k}(z)} = {\sum\limits_{i = 1}^{N_{fbf}}{d_{k}^{i}z^{- i}}}},$

[0025] where N_(fbf) is the number of tap coefficients in FBF 20, asalso defined above.

[0026] For FIR filters, it is convenient to describe their operation invector and matrix notation. Accordingly, we define the vector of FFFcoefficients for adaptive DFE 12 as

b′ _(k)=└b_(k) ¹ . . . b_(k) ^(M)b_(k) ^(M+1) . . . b_(k) ^(N) ^(_(fff))┘,

[0027] where M is the main (or decision) tap of the FFF. A vector ofpast input samples to FFF 14 is defined as

r′ _(k)=└R_(k−1)R_(k−2) . . . R_(k−N) _(fff) ┘.

[0028] The output of FFF 14, U_(k), is thus equal to

U _(k) =b′ _(k) ·r _(k).

[0029] We define the vector of coefficients for FBF 20 as

d′ _(k)=└d_(k) ¹d_(k) ² . . . d_(k) ^(N) ^(_(fbf)) ┘

[0030] and a vector of past input samples to FBF 20 as

x′ _(k)=└X_(k−1)X_(k−2) . . . X_(k−N) _(fbf) ┘.

[0031] Assuming that slicer 26 makes correct decisions (i.e., X_(k) isequal to A_(k−M)), then the output of FBF 20, Q_(k), is equal to

Q _(k) =d′ _(d) ·x _(k).

[0032] The output of adaptive equalizer 12, namely Y_(k), is obtained byadding outputs of FFF 14 and FBF 20, as follows

Y _(k) =U _(k) +Q _(k).

[0033] The decision error, E_(k), is equal to the difference of therecovered signal X_(k) and the output Y_(k)

E _(k) =X _(k) −Y _(k).

[0034] In this example, the decision error is equal to the true error,since correct decisions are assumed.

[0035] The LMS tap update equation for FBF 20 is

d′ _(k) =d′ _(k−1) +α·E _(k) ·x′ _(k,)

[0036] where i is the tap index and a is the LMS step size of FBF 20.The LMS tap update equations for FFF 14 are:

b _(k) ^(l) =b _(k−1) ^(l)+β₁ ·E _(k) ·R _(k−l), i=1, . . . , M

b _(k) ^(l) =b _(k−1) ^(l)+β₂ ·E _(k−L) ·V _(k−l−L), i=M+1, . . . ,N_(fff)

[0037] where i is the tap index and β₁ and β₂ are the LMS step sizes ofFFF 14.

[0038] Adaptive DFE 12 generates the noise estimate V_(k) by subtractinga replica of the signal R_(k) from a delayed version of that signal plusnoise. The signal replica is constructed by filtering X_(k) using CE 32.CE 32, as noted, is an FIR filter with the following z-domain response${{G_{k}(z)} = {\sum\limits_{i = 1}^{N_{ce}}{g_{k}^{i}z^{- i}}}},$

[0039] where N_(ce) is the number of tap coefficients in the CE.

[0040] We define the vector of coefficients for CE 32 as

′ _(k)=└g_(k) ¹g_(k) ² . . . g_(k) ^(N) ^(_(ce)) ┘

[0041] and a vector of past input samples to CE 32 as

x′_(CE) _(k) =└X_(k−1)X_(k−2) . . . X_(k−N) _(ce) ┘.

[0042] The output of CE 32, namely T_(k), is thus equal to

T _(k) =g′ _(k) ·x_(CE) _(k) .

[0043] The signal estimate T_(k) is a delayed estimate of the signalcomponent of R_(k). T_(k) is an estimate of the signal component ofR_(k−M−L). The estimate is delayed by M+L samples, where L, as notedabove, is the number of precursor samples to be replicated by CE 32.

[0044] The output, V_(k−M−L), of the CE summing node 38 is obtained bysubtracting T_(k) from R_(k−M−L), as follows

V _(k−M−L) =R _(k−M−L) −T _(k).

[0045] V_(k−M−L) contains both additive noise and a residual signalcomponent. V_(k−M−L) is thus a relatively accurate estimate of theadditive noise when the number of CE taps is sufficient and the CEcoefficients have been adapted to the channel.

[0046] The LMS process adaptively updates the CE coefficients. The tapupdate equations (in vector notation) for CE 32 are

g _(k) =g _(k−1) +γV _(k−M−L) ·x_(CE) _(k) ,

[0047] where γ is the CE LMS step size.

[0048] The LMS step sizes of adaptive DFE 12 may be optimized withrespect to its signal-to-noise ratio (SNR). The LMS step sizes α and β₁are bounded by the eigenvalues of the filter and the desired tapfluctuation error. To keep the gain of taps M+1 to N_(fff) of FFF 14,with respect to the noise, equivalent to the gain of FBF 20, withrespect to the ISI, the LMS step size β₂ may be increased by a factorequal to the SNR. For example, assume the SNR at the input to slicer 26is 30 decibels (dB), then

β₂=(10^(30/20))*β₁.

[0049] Adaptive DFE 12 represents only one embodiment of the invention;other embodiments exist. For example, the use of CE 32 is only onepossible way of obtaining the noise or noise estimate. When othermethods of obtaining the noise or noise estimate are used, the FFF tapupdate equations may be slightly modified, e.g., in terms of the timeindices of the decision error and the noise estimate.

[0050] The invention may also be used with a fractionally-spaced FFF. Inthis case, the noise is estimated at the fractional sampling rate of theFFF. This can be done by utilizing multiple CE filters, each operatingat the symbol rate, or one CE filter operating at the fractionalsampling rate.

[0051] The invention is described here for a real, basebandcommunications system, however, it is also valid for a complex orpassband system. The tap update equations may be slightly modified, inthis case, to account for complex arithmetic and to include conjugationof the data.

[0052] The coefficients b_(k) ^(i), d_(k) ^(i) and g_(k) ^(i), describedabove, may be adaptively determined using hardware, e.g., discretehardware components such as programmable logic gates, or softwarerunning on a computer. FIG. 3 shows a computer 40 on which thecoefficients may be determined. Computer 40 includes a processor 42, amemory 44, and a storage medium 46 (see view 48). Storage medium 46stores machine-executable instructions 50 that are executed by processor42 out of memory 44 to adaptively determine the coefficients.

[0053] Although a personal computer is shown in FIG. 3, the invention isnot limited to use with the hardware and software of FIG. 3. It may findapplicability in any computing or processing environment. Thecoefficients may be determined using hardware, software, or acombination of the two. The coefficients may be determined usingcomputer programs executing on programmable computers or other machinesthat each include a processor, a storage medium readable by theprocessor (including volatile and non-volatile memory and/or storagecomponents), at least one input device, and one or more output devices.Program code may be applied to data entered using an input device (e.g.,a mouse or keyboard) to determine the coefficients.

[0054] Each such program may be implemented in a high level proceduralor object-oriented programming language to communicate with a computersystem. However, the programs can be implemented in assembly or machinelanguage. The language may be a compiled or an interpreted language.

[0055] Each computer program may be stored on a storage medium/article(e.g., CD-ROM, hard disk, or magnetic diskette) that is readable by ageneral or special purpose programmable computer for configuring andoperating the computer when the storage medium or device is read by thecomputer to determine the coefficients. The coefficients may bedetermined using a machine-readable storage medium, configured with acomputer program, where, upon execution, instructions in the computerprogram cause a machine to determine the coefficients.

[0056] The invention is not limited to the specific embodimentsdescribed above. For example, the invention is not limited to use withFIR filters or to use with the particular configuration shown in FIG. 2.The adaptive equalizer may be implemented in a single pair high speeddigital subscriber line (HDSL2/G.SHDSL) system, or any other signaltransmission system that requires reduction in ISI and colored noise.

[0057] Alternatively, the coefficients b_(k) ^(i) may be generated basedon the input signal alone, i.e., not the noise. This is called thezeroforcing (ZF) criterion.

[0058] Other embodiments not described herein are also within the scopeof the following claims.

What is claimed is:
 1. A method of generating coefficients for use in anadaptive equalizer, the method comprising: generating first coefficientsfor use by the adaptive equalizer to reduce pre-cursor intersymbolinterference in an input signal; and generating second coefficients foruse by the adaptive equalizer to whiten noise in the input signal. 2.The method of claim 1, wherein the first and second coefficients areused, respectively, in first and second sets of taps in a finite impulseresponse feedforward filter.
 3. The method of claim 2, wherein the firstcoefficients are generated based on the input signal and noise.
 4. Themethod of claim 2, wherein the second coefficients are generated basedon an estimate of the noise.
 5. The method of claim 3, wherein the noiseis estimated by subtracting a substantial replica of the input signalfrom a delayed version of the input signal and noise.
 6. The method ofclaim 1, wherein the first coefficients, b_(K) ^(i), are generated asfollows: b _(k) ^(i) =b _(k−1) ^(i)+β₁ ·E _(k) ·R _(k−i), for i=1 to M,where i is an index of taps in a feedforward filter in the adaptiveequalizer, β₁ is a step size of the feedforward filter, E_(k) is anerror signal generated by the adaptive equalizer, R_(k−i) is thecombined input signal and noise fed to the adaptive equalizer, and M isa number of taps in the feedforward filter between a first tap and amain tap.
 7. The method of claim 1, wherein the second coefficients,b_(K) ^(i), are generated as follows: b _(k) ^(i) =b _(k−1) ^(i)+β₂ ·E_(k−L) ·V _(k−i−L), for i=M+1 to N_(fff), where i is an index of taps ina feedforward filter in the adaptive equalizer, β₂ is a step size of thefeedforward filter, E_(k−L) is a delayed error signal generated by theadaptive equalizer, V_(k−i−L) is an estimate of noise fed to theadaptive equalizer, M is a number of taps in the feedforward filterbetween a first tap and a main tap, and N_(fff) is a total number oftaps in the feedforward filter.
 8. An article comprising amachine-readable medium that stores instructions for generatingcoefficients for use in an adaptive equalizer, the instructions causinga machine to: generate first coefficients for use by the adaptiveequalizer to reduce pre-cursor intersymbol interference in an inputsignal; and generate second coefficients for use by the adaptiveequalizer to whiten noise in the input signal.
 9. The article of claim8, wherein the first and second coefficients are used, respectively, infirst and second sets of taps in a finite impulse response feedforwardfilter.
 10. The article of claim 9, wherein the first coefficients aregenerated based on the input signal and noise and the secondcoefficients are generated based on an estimate of the noise.
 11. Thearticle of claim 10, wherein the noise is estimated by subtracting asubstantial replica of the input signal from a delayed version of theinput signal and noise.
 12. The article of claim 8, wherein the firstcoefficients, b_(K) ^(i), are generated as follows: b _(k) ^(i) =b_(k−1) ^(i)+β₁ ·E _(k) ·R _(k−i), for i=1 to M, where i is an index oftaps in a feedforward filter in the adaptive equalizer, β₁ is a stepsize of the feedforward filter, E_(k) is an error signal generated bythe adaptive equalizer, R_(k−i) is the combined input signal and noisefed to the adaptive equalizer, and M is a number of taps in thefeedforward filter between a first tap and a main tap.
 13. The articleof claim 8, wherein the second coefficients, b_(K) ^(i), are generatedas follows: b _(k) ^(i) =b _(k−1) ^(i)+β₂ ·E _(k−L) ·V _(k−i−L), fori=M+1 to N_(fff), where i is an index of taps in a feedforward filter inthe adaptive equalizer, β₂ is a step size of the feedforward filter,E_(k−L) is a delayed error signal generated by the adaptive equalizer,V_(k−i−L) is an estimate of noise fed to the adaptive equalizer, M is anumber of taps in the feedforward filter between a first tap and a maintap, and N_(fff) is a total number of taps in the feedforward filter.14. An adaptive equalizer comprising circuitry which: generates firstcoefficients for use by the adaptive equalizer to reduce pre-cursorintersymbol interference in an input signal; and generates secondcoefficients for use by the adaptive equalizer to whiten noise in theinput signal.
 15. The adaptive equalizer of claim 14, wherein the firstand second coefficients are used, respectively, in first and second setsof taps in a finite impulse response feedforward filter.
 16. Theadaptive equalizer of claim 15, wherein the first coefficients aregenerated based on the input signal and noise and the secondcoefficients are generated based on an estimate of the noise.
 17. Theadaptive equalizer of claim 16, wherein the noise is estimated bysubtracting a substantial replica of the input signal from a delayedversion of the input signal and noise.
 18. The adaptive equalizer ofclaim 14, wherein the first coefficients, b_(K) ^(i), are generated asfollows: b _(k) ^(i) =b _(k−1) ^(i)+β₁ ·E _(k) ·R _(k−i), for i=1 to M,where i is an index of taps in a feedforward filter in the adaptiveequalizer, β₁ is a step size of the feedforward filter, E_(k) is anerror signal generated by the adaptive equalizer, R_(k−i) is thecombined input signal and noise fed to the adaptive equalizer, and M isa number of taps in the feedforward filter between a first tap and amain tap.
 19. The adaptive equalizer of claim 14, wherein the secondcoefficients, b_(K) ^(i), are generated as follows: b _(k) ^(i) =b_(k−1) ^(i)+β₂ ·E _(k−L) ·V _(k−i−L), for i=M+1 to N_(fff), where i isan index of taps in a feedforward filter in the adaptive equalizer, β₂is a step size of the feedforward filter, E_(k−L) is a delayed errorsignal generated by the adaptive equalizer, V_(k−i−L) is an estimate ofnoise fed to the adaptive equalizer, M is a number of taps in thefeedforward filter between a first tap and a main tap, and N_(fff) is atotal number of taps in the feedforward filter.
 20. The adaptiveequalizer of claim 14, wherein the circuitry comprises a memory thatstores machine-executable instructions and a processor that executes theinstructions to generate the first and second coefficients.
 21. Theadaptive equalizer of claim 14, wherein the circuitry comprises discretehardware components that are configured to generate the first and secondcoefficients.
 22. The adaptive equalizer of claim 14, wherein thediscrete hardware components include logic gates.
 23. An adaptiveequalizer which processes an input signal that includes noise,pre-cursor intersymbol interference, and post-cursor intersymbolinterference, the adaptive equalizer comprising: a feedforward filterwhich reduces the pre-cursor intersymbol interference and whitens thenoise; a feedback filter which obtains the post-cursor intersymbolinterference in a signal that corresponds to the input signal; andcircuitry which removes the post-cursor intersymbol interference fromthe input signal; wherein the feedforward filter includes separate firstand second coefficients, the first coefficients to reduce the pre-cursorintersymbol interference and the second coefficients to whiten thenoise.
 24. The adaptive equalizer of claim 23, wherein the first andsecond coefficients are used, respectively, in first and second sets oftaps of the feedforward filter.
 25. The adaptive equalizer of claim 24,wherein the feedforward filter generates the first coefficients based onthe input signal and the noise and generates the second coefficientsbased on an estimate of the noise.
 26. The adaptive equalizer of claim25, further comprising circuitry which estimates the noise bysubtracting a substantial replica of the input signal from a delayedversion of the input signal.
 27. The adaptive equalizer of claim 23,wherein the first coefficients, b_(K) ^(i), are generated as follows: b_(k) ^(i) =b _(k−1) ^(i)+β₁ ·E _(k) ·R _(k−i), for i=1 to M, where i isan index of taps in the feedforward filter, β₁ is a step size of thefeedforward filter, E_(k) is an error signal generated by the adaptiveequalizer, R_(k−i) is the input signal including the noise, and M is anumber of taps in the feedforward filter between a first tap and a maintap.
 28. The adaptive equalizer of claim 23, wherein the secondcoefficients, b_(K) ^(i), are generated as follows: b _(k) ^(i) =b_(k−1) ^(i)+β₂ ·E _(k−L) ·V _(k−i−L), for i=M+1 to N_(fff), where i isan index of taps in the feedforward filter, β₂ is a step size of thefeedforward filter, E_(k−L) is a delayed error signal generated by theadaptive equalizer, V_(k−i−L) is an estimate of the noise, M is a numberof taps in the feedforward filter between a first tap and a main tap,and N_(fff) is a total number of taps in the feedforward filter.
 29. Theadaptive equalizer of claim 23, wherein the adaptive equalizer comprisesa single pair high speed digital subscriber line equalizer.